Symmetric Arithmetic Circuits.
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Dawar, Anuj https://orcid.org/0000-0003-4014-8248
Wilsenach, Gregory
Abstract
We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the restriction amounts to requiring that the shape of the circuit is invariant under row and column permutations of the matrix. We establish unconditional, nearly exponential, lower bounds on the size of any symmetric circuit for computing the permanent over any field of characteristic other than 2. In contrast, we show that there are polynomial-size symmetric circuits for computing the determinant over fields of characteristic zero.
Description
Keywords
Journal Title
ICALP
Conference Name
47th International Colloquium on Automata, Languages, and Programming
Journal ISSN
1868-8969
Volume Title
168
Publisher
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/S03238X/1)